I play vintage baseball and we only use one umpire who stations himself about 10 feet in foul territory down either the 1st or 3rd base line depending on whether the batter bats lefty or rights. Foul tips caught either in the air or on one bounce are an out. Players are usually on the honor system but the umpire can see/hear a foul tip too. I've heard them from 40 feet away. Of course we don't play in front of thousands of people but, like most calls, they can always go to replay.
Only the defense can appeal a checked swing so any appeal is when the plate umpire says it wasn't a swing. On the bases, the base umpire may or may not have seen the runner miss a base or leave the base too soon. They are supposed to look - especially on sac flies - but they won't sY anything unless the defense appeals.